{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A demo of K-Means clustering on the handwritten digits data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adapted from http://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_digits.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we compare the various initialization strategies for K-means in terms of runtime and quality of the results.\n",
    "\n",
    "As the ground truth is known here, we also apply different cluster quality metrics to judge the goodness of fit of the cluster labels to the ground truth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Method definition require(Symbol) in module Base at loading.jl:345 overwritten in module Main at /Users/cedric/.julia/v0.5/Requires/src/require.jl:12.\n"
     ]
    }
   ],
   "source": [
    "using PyPlot    # Pkg.add(\"PyPlot\") to install\n",
    "using ScikitLearn\n",
    "using PyCall\n",
    "using ScikitLearn.Utils: meshgrid\n",
    "\n",
    "@sk_import cluster: KMeans\n",
    "@sk_import datasets: load_digits\n",
    "@sk_import decomposition: PCA\n",
    "@pyimport sklearn.metrics as metrics\n",
    "@pyimport sklearn.preprocessing as preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_digits: 10, \t n_samples 1797, \t n_features 64\n",
      "____________________________________________________________________________\n",
      "init    time  inertia    homo   compl  v-meas     ARI AMI  silhouette\n",
      "k-means++   0.25s    69684   0.678   0.717   0.697   0.569   0.674    0.124\n",
      "   random   0.21s    69672   0.683   0.722   0.702   0.574   0.680    0.140\n",
      "PCA-based   0.03s    70804   0.671   0.698   0.684   0.561   0.668    0.122\n",
      "____________________________________________________________________________"
     ]
    }
   ],
   "source": [
    "srand(42)\n",
    "\n",
    "digits = load_digits()\n",
    "data = preprocessing.scale(digits[\"data\"])\n",
    "\n",
    "n_samples, n_features = size(data)\n",
    "n_digits = length(unique(digits[\"target\"]))\n",
    "labels = digits[\"target\"]\n",
    "\n",
    "sample_size = 300\n",
    "\n",
    "@printf(\"n_digits: %d, \\t n_samples %d, \\t n_features %d\\n\", n_digits, n_samples, n_features)\n",
    "\n",
    "\n",
    "println(\"____________________________________________________________________________\")\n",
    "@printf(\"% 9s\", \"init    time  inertia    homo   compl  v-meas     ARI AMI  silhouette\\n\")\n",
    "\n",
    "function bench_k_means(estimator, name, data)\n",
    "    t0 = time()\n",
    "    fit!(estimator, data)\n",
    "    @printf(\"% 9s   %.2fs    %i   %.3f   %.3f   %.3f   %.3f   %.3f    %.3f\\n\",\n",
    "            name, time()-t0, estimator[:inertia_],\n",
    "            metrics.homogeneity_score(labels, estimator[:labels_]),\n",
    "            metrics.completeness_score(labels, estimator[:labels_]),\n",
    "            metrics.v_measure_score(labels, estimator[:labels_]),\n",
    "            metrics.adjusted_rand_score(labels, estimator[:labels_]),\n",
    "            metrics.adjusted_mutual_info_score(labels,  estimator[:labels_]),\n",
    "            metrics.silhouette_score(data, estimator[:labels_],\n",
    "                                      metric=\"euclidean\",\n",
    "                                      sample_size=sample_size))\n",
    "end\n",
    "\n",
    "bench_k_means(KMeans(init=\"k-means++\", n_clusters=n_digits, n_init=10),\n",
    "              \"k-means++\", data)\n",
    "\n",
    "bench_k_means(KMeans(init=\"random\", n_clusters=n_digits, n_init=10),\n",
    "              \"random\", data)\n",
    "\n",
    "# in this case the seeding of the centers is deterministic, hence we run the\n",
    "# kmeans algorithm only once with n_init=1\n",
    "pca = fit!(PCA(n_components=n_digits), data)\n",
    "bench_k_means(KMeans(init=pca[:components_], n_clusters=n_digits, n_init=1),\n",
    "              \"PCA-based\",\n",
    "              data)\n",
    "print(\"____________________________________________________________________________\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject <class 'sklearn.cluster.k_means_.KMeans'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels = KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/cedric/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/cedric/.julia/v0.5/PyCall/src/PyCall.jl\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1797-element Array{Int32,1}:\n",
       " 3\n",
       " 2\n",
       " 2\n",
       " 9\n",
       " 0\n",
       " 9\n",
       " 4\n",
       " 1\n",
       " 9\n",
       " 9\n",
       " 3\n",
       " 6\n",
       " 7\n",
       " ⋮\n",
       " 1\n",
       " 9\n",
       " 9\n",
       " 0\n",
       " 2\n",
       " 2\n",
       " 0\n",
       " 9\n",
       " 3\n",
       " 2\n",
       " 9\n",
       " 9"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit!(KMeans(init=pca[:components_], n_clusters=n_digits, n_init=1), data)[:labels_]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x324991350>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(Any[],Any[])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###############################################################################\n",
    "# Visualize the results on PCA-reduced data\n",
    "\n",
    "reduced_data = fit_transform!(PCA(n_components=2), data)\n",
    "kmeans = KMeans(init=\"k-means++\", n_clusters=n_digits, n_init=10)\n",
    "fit!(kmeans, reduced_data)\n",
    "\n",
    "# Step size of the mesh. Decrease to increase the quality of the VQ.\n",
    "h = .02     # point in the mesh [x_min, m_max]x[y_min, y_max].\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "x_min, x_max = minimum(reduced_data[:, 1]) - 1, maximum(reduced_data[:, 1]) + 1\n",
    "y_min, y_max = minimum(reduced_data[:, 2]) - 1, maximum(reduced_data[:, 2]) + 1\n",
    "xx, yy = meshgrid(x_min:h:x_max, y_min:h:y_max);\n",
    "\n",
    "# Obtain labels for each point in mesh. Use last trained model.\n",
    "Z = predict(kmeans, hcat(xx[:], yy[:]))\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = reshape(Z, size(xx)...)\n",
    "\n",
    "imshow(Z, interpolation=\"nearest\",\n",
    "        extent=(minimum(xx), maximum(xx), minimum(yy), maximum(yy)),\n",
    "       cmap=PyPlot.cm[:Paired],\n",
    "       aspect=\"auto\", origin=\"lower\")\n",
    "\n",
    "plot(reduced_data[:, 1], reduced_data[:, 2], \"k.\", markersize=2)\n",
    "# Plot the centroids as a white X\n",
    "centroids = kmeans[:cluster_centers_]\n",
    "scatter(centroids[:, 1], centroids[:, 2],\n",
    "        marker=\"x\", s=169, linewidths=3,\n",
    "        color=\"w\", zorder=10)\n",
    "title(\"K-means clustering on the digits dataset (PCA-reduced data)\\n\"*\"Centroids are marked with white cross\")\n",
    "xlim(x_min, x_max)\n",
    "ylim(y_min, y_max)\n",
    "xticks(())\n",
    "yticks(())"
   ]
  }
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